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61.
Eulerjevi in Hamiltonovi grafi pri pouku v osnovni in srednji šoli
Kristina Plavec, 2017, magistrsko delo

Opis: V magistrskem delu obravnavam izbrana poglavja iz teorije grafov in sicer Eulerjeve in Hamiltonove grafe. V prvem delu navajam potrebne definicije, trditve in izreke z dokazi. Podani so tudi osnovni pojmi, ki se navezujejo na ti dve vsebini. V drugem delu pa podajam primer priprave za obravnavo izbranih vsebin v osnovni in srednji šoli. Priprave vsebujejo vsebinsko-metodične napotke ter napotke glede izbire učne oblike in metode.
Ključne besede: teorija grafov v osnovnošolskem in srednješolskem izobraževanju, Eulerjevi grafi, Hamiltonovi grafi
Objavljeno: 19.07.2017; Ogledov: 63; Prenosov: 21
.pdf Polno besedilo (2,34 MB)

62.
Optimal distribution of incentives for public cooperation in heterogeneous interaction environments
Xiaojie Chen, Matjaž Perc, 2014, izvirni znanstveni članek

Opis: In the framework of evolutionary games with institutional reciprocity, limited incentives are at disposal for rewarding cooperators and punishing defectors. In the simplest case, it can be assumed that, depending on their strategies, all players receive equal incentives from the common pool. The question arises, however, what is the optimal distribution of institutional incentives? How should we best reward and punish individuals for cooperation to thrive? We study this problem for the public goods game on a scale-free network. We show that if the synergetic effects of group interactions are weak, the level of cooperation in the population can be maximized simply by adopting the simplest "equal distribution" scheme. If synergetic effects are strong, however, it is best to reward high-degree nodes more than low-degree nodes. These distribution schemes for institutional rewards are independent of payoff normalization. For institutional punishment, however, the same optimization problem is more complex, and its solution depends on whether absolute or degree-normalized payoffs are used. We find that degree-normalized payoffs require high-degree nodes be punished more lenient than low-degree nodes. Conversely, if absolute payoffs count, then high-degree nodes should be punished stronger than low-degree nodes.
Ključne besede: public cooperation, institutional reciprocity, scale-free network, punishment, reward
Objavljeno: 10.07.2017; Ogledov: 67; Prenosov: 0
.pdf Polno besedilo (3,26 MB)

63.
Linear recognition of generalized Fibonacci cubes $Q_h (111)$
Yoomi Rho, Aleksander Vesel, 2016, izvirni znanstveni članek

Opis: The generalized Fibonacci cube $Q_h(f)$ is the graph obtained from the $h$-cube $Q_h$ by removing all vertices that contain a given binary string $f$ as a substring. In particular, the vertex set of the 3rd order generalized Fibonacci cube $Q_h(111)$ is the set of all binary strings $b_1b_2 ... b_h$ containing no three consecutive 1’s. We present a new characterization of the 3rd order generalized Fibonacci cubes based on their recursive structure. The characterization is the basis for an algorithm which recognizes these graphs in linear time.
Ključne besede: graph theory, Fibonacci cubes, recognition algorithm
Objavljeno: 10.07.2017; Ogledov: 61; Prenosov: 1
.pdf Polno besedilo (803,81 KB)

64.
Guarded subgraphs and the domination game
Gašper Košmrlj, Douglas F. Rall, Sandi Klavžar, Boštjan Brešar, 2015, izvirni znanstveni članek

Opis: V članku vpeljemo koncept zaščitenega podgrafa. Množica le-teh po definicji leži med množico konveksnih in 2-izometričnih podgrafov, hkrati pa ni primerljiva z množico izometričnimih podgrafov. Dokažemo nekatere metrične lastnosti zaščitenih podgrafov ter koncept uporabimo v dominacijski igri, v kateri dva igralca, Dominator in Zavlačevalka, izmenično izbirata vozlišča grafa, tako da vsako izbrano vozlišče poveča množico dominiranih vozlišč. Dominatorjev cilj je končati igro, tj. dominirati celoten graf, čim hitreje, medtem ko je Zavlačevalkin cilj odigrati čim več potez. Igralno dominacijsko število je število potez v igri, ko Dominator začne in oba igralca igrata optimalno. Kot glavni rezultat članka dokažemo, da igralno dominacijsko število grafa ni nikoli manjše, kot igralno dominacijsko število njegovega zaščitenega podgrafa. Predstavljenih je tudi več aplikacij tega rezultata.
Ključne besede: dominacijska igra, igralno dominacijsko številko, konveksni podgraf, (2-)izometrični podgraf
Objavljeno: 10.07.2017; Ogledov: 49; Prenosov: 0
.pdf Polno besedilo (690,85 KB)

65.
Covering codes in Sierpiński graphs
Michel Mollard, Laurent Beaudou, Sandi Klavžar, Sylvain Gravier, Matjaž Kovše, 2010, izvirni znanstveni članek

Opis: Za dani graf ▫$G$▫ in celi števili ▫$a$▫ in ▫$b$▫ je ▫$(a,b)$▫-koda grafa ▫$G$▫ množica vozlišč ▫$C$▫, tako da ima vsako vozlišče iz ▫$C$▫ natanko ▫$a$▫ sosedov v ▫$C$▫, vsako drugo vozlišče pa natanko ▫$b$▫ sosedov v ▫$C$▫. V tem prispevku klasificiramo števila ▫$a$▫ in ▫$b$▫, za katera obstajajo ▫$(a,b)$▫-kode v grafih Sierpińskega.
Ključne besede: graph theory, codes in graphs, perfect codes, Sierpiński graphs
Objavljeno: 10.07.2017; Ogledov: 51; Prenosov: 1
.pdf Polno besedilo (786,68 KB)

66.
Connectivity of Fibonacci cubes, Lucas cubes, and generalized cubes
Jernej Azarija, Sandi Klavžar, Jaehun Lee, Yoomi Rho, 2015, izvirni znanstveni članek

Opis: If ▫$f$▫ is a binary word and ▫$d$▫ a positive integer, then the generalized Fibonacci cube ▫$Q_d(f)$▫ is the graph obtained from the ▫$d$▫-cube ▫$Q_d$▫ by removing all the vertices that contain ▫$f$▫ as a factor, while the generalized Lucas cube ▫$Q_d(\stackrel{\leftharpoondown}{f})$▫ is the graph obtained from ▫$Q_d$▫ by removing all the vertices that have a circulation containing ▫$f$▫ as a factor. The Fibonacci cube ▫$\Gamma_d$▫ and the Lucas cube ▫$\Lambda_d$▫ are the graphs ▫$Q_d({11})$▫ and ▫$Q_d(\stackrel{\leftharpoondown}{11})$▫, respectively. It is proved that the connectivity and the edge-connectivity of ▫$\Gamma_d$▫ as well as of ▫$\Lambda_d$▫ are equal to ▫$\left\lfloor \frac{d+2}{3}\right\rfloor$▫. Connected generalized Lucas cubes are characterized and generalized Fibonacci cubes are proved to be 2-connected. It is asked whether the connectivity equals minimum degree also for all generalized Fibonacci/Lucas cubes. It was checked by computer that the answer is positive for all ▫$f$▫ and all ▫$d \le9$▫.
Ključne besede: Fibonacci cube, Lucas cube, generalized Fibonacci cube, generalized Lucas cube, connectivity, combinatorics on words
Objavljeno: 10.07.2017; Ogledov: 48; Prenosov: 0
.pdf Polno besedilo (740,04 KB)

67.
A new characterization and a recognition algorithm of Lucas cubes
Andrej Taranenko, 2013, izvirni znanstveni članek

Opis: Fibonacci and Lucas cubes are induced subgraphs of hypercubes obtained by excluding certain binary strings from the vertex set. They appear as models for interconnection networks, as well as in chemistry. We derive a characterization of Lucas cubes that is based on a peripheral expansion of a unique convex subgraph of an appropriate Fibonacci cube.This serves as the foundation for a recognition algorithm of Lucas cubes that runs in linear time.
Ključne besede: graph theory, Lucas cubes, characterization, recognition algorithm
Objavljeno: 10.07.2017; Ogledov: 66; Prenosov: 0
.pdf Polno besedilo (563,10 KB)

68.
Biology students' teacher opinions about the integration of ICT into the learning and teaching process
Andreja Špernjak, 2014, izvirni znanstveni članek

Opis: Biology laboratory work can be performed in various ways, even using information and communication technologies (ICT). Whether a teacher incorporates it into laboratory work is related to different factors, but educators can influence students’ beliefs about the value of ICT through their pedagogical practice. In our study, student teachers of biology gave opinions on how successfully university professors use ICT in the classroom, where they acquired most knowledge about ICT and their attitude towards using of ICT in laboratory work. Student teachers were critical about the knowledge and usage of ICT of university professors in class. During their student teachers mostly failed to acquire knowledge about ICT and practice in incorporating it into daily routines. These results will be presented to our university professors, at which time we will suggest how they could use ICT more effectively in daily practice because, on the one hand, they are responsible for students teacher attitudes and for the level of student teacher knowledge, while, on the others, they precipitate indirectly in forming the pupils’ attitudes and determining the level of the pupils’ knowledge of ICT. The study was done on 85 student teachers of biology. Attitudes toward ICT are statistically significant by gender.
Ključne besede: education, information and communication technology, ICT, gender studies
Objavljeno: 06.07.2017; Ogledov: 53; Prenosov: 0
.pdf Polno besedilo (166,92 KB)

69.
Vortices determine the dynamics of biodiversity in cyclical interactions with protection spillovers
Matjaž Perc, Attila Szolnoki, 2015, izvirni znanstveni članek

Opis: If rock beats scissors and scissors beat paper, one might assume that rock beats paper too. But this is not the case for intransitive relationships that make up the famous rock-paper-scissors game. However, the sole presence of paper might prevent rock from beating scissors, simply because paper beats rock. This is the blueprint for the rock-paper-scissors game with protection spillovers, which has recently been introduced as a new paradigm for biodiversity in well-mixed microbial populations. Here we study the game in structured populations, demonstrating that protection spillovers give rise to spatial patterns that are impossible to observe in the classical rock-paper-scissors game.Weshow that the spatiotemporal dynamics of the system is determined by the density of stable vortices, which may ultimately transform to frozen states, to propagating waves, or to target waves with reversed propagation direction, depending further on the degree and type of randomness in the interactions among the species. If vortices are rare, the fixation to waves and complex oscillatory solutions is likelier. Moreover, annealed randomness in interactions favors the emergence of target waves, while quenched randomness favors collective synchronization. Our results demonstrate that protection spillovers may fundamentally change the dynamics of cyclic dominance in structured populations, and they outline the possibility of programming pattern formation in microbial populations.
Ključne besede: cyclical interactions, pattern formation, vortices, phase transitions, selforganization, biodiversity
Objavljeno: 03.07.2017; Ogledov: 53; Prenosov: 2
.pdf Polno besedilo (1,32 MB)

70.
Self-organization towards optimally interdependent networks by means of coevolution
Zhen Wang, Attila Szolnoki, Matjaž Perc, 2014, izvirni znanstveni članek

Opis: Coevolution between strategy and network structure is established as a means to arrive at the optimal conditions needed to resolve social dilemmas. Yet recent research has highlighted that the interdependence between networks may be just as important as the structure of an individual network. We therefore introduce the coevolution of strategy and network interdependence to see whether this can give rise to elevated levels of cooperation in the prisonerʼs dilemma game. We show that the interdependence between networks self-organizes so as to yield optimal conditions for the evolution of cooperation. Even under extremely adverse conditions, cooperators can prevail where on isolated networks they would perish. This is due to the spontaneous emergence of a two-class society, with only the upper class being allowed to control and take advantage of the interdependence. Spatial patterns reveal that cooperators, once arriving at the upper class, are much more competent than defectors in sustaining compact clusters of followers. Indeed, the asymmetric exploitation of interdependence confers to them a strong evolutionary advantage that may resolve even the toughest of social dilemmas.
Ključne besede: coevolution, cooperation, interdependent networks, evolutionary games, collective phenomena, self-organization, phase transitions, physics of social systems
Objavljeno: 03.07.2017; Ogledov: 44; Prenosov: 1
.pdf Polno besedilo (887,51 KB)

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